存在趋势和周期特征的非平稳时间序列的建模及其应用

本文研究存在未知周期和趋势的非平稳时间序列的估计问题.将经典的时间序列分解模型写成一个含有未知参数的部分线性模型,首先采用B-样条逼近未知时间趋势,然后利用惩罚最小二乘回归法得到未知周期、周期序列和趋势的估计.本文还给出估计量的理论性质,包括周期估计的相合性以及周期序列和趋势估计的渐近性质.模拟研究展现了本文方法的优越...     

不等长周期时间序列的周期划分方法

针对时间序列周期不等长的情况,提出了一种基于周期划分的时间序列周期分析方法.首先将时间序列变换到频域中获取序列的周期特征,其次根据周期特征计算移动平均的项数来对时间序列做移动平均处理,然后计算移动平均处理后序列中的极值点,最后对极值点按条件进行剔除后得到周期划分点.以划分点为界划分得到时间序列的多个周期段,经过分析采用周期段的中位数线来表示时间序列的周期性变化特征.这种周期划分方法更适用于存在随机波动的长序列,实验表明该方法能较好地对序列做出划分,得到的周期段中位数线的变化特点也与原时间序列基本相符.     

一类广义耦合的非线性波动方程组时间周期解的存在性

研究了一类广义耦合的非线性波动方程组关于时间周期解的问题.首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Laray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

基于谱分析的非平稳时间序列中的潜周期研究

时间序列的频域分析并不如时域分析应用广泛,但其弥补了时域分析的不足:能够把时间序列分解为具有不同振幅,相位和频率的周期分量的叠加,找出原序列中隐含的主要周期分量,并从周期波动的角度对序列进行解释.针对非平稳时间序列进行研究,利用B样条函数为基底并引入惩罚项,提取序列中的趋势项之后,再根据样本谱密度理论得到时序数据中的潜周期,最终将原始时间序列分解为趋势项,周期项和随机扰动项.数据模拟部分验证了通过B样条估计并提取的趋势项具有较高的精确度,并会对周期项的提取产生积极的影响.实际数据部分使用了黄金价格的月度数据,得到了长,中,短三个波动周期这一有意义的结论,验证了本方法的可行性和有效性.     

带逐段常变量的微分方程的概周期解

本文研究相关差分方程的概周期序列解,并以此为工具得出带逐段常变量的微分方程的概周期解的若干存在性定理．     

二元序列的自相关函数和游程的一些结果

给出了二元周期序列的自相关性质与其游程性质之间的关系,作为一个应用,我们给出了周期为1 2的零自相关窗大于等于6的所有序列.     

q元m序列非周期自相关函数的估计与M序列的分段线性化

序列的非周期自相关函数的估计,具有良好非周期自相关性的序列的构造,以及非线性M序列的相关性等方面已有的成果较少.著名的Barker序列当长度大于13时是否存在的问题尚未完全解决,L序列的非周期自相关函数的估计仅在长度较短时有一些数值计算结果,文献曾估计了一类二元序列非周期自相关函数的上界.最近,章照止巧妙地应用组合数学方法估计了状态两两不同的二元序列中一元的个数(在这基础     

一类KdV非线性Schr(o)dinger组合微分方程组时间周期解的存在性

本文研究了一类KdV非线性Schr(o)dinger组合微分方程组时间周期解的问题,首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Leray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

M序列一个周期的复杂度

在流密码中,M序列及M序列一个周期复杂度是一个重要课题。Chan等人在文献[2]中对M序列的界和分布进行了讨论。本文将对M序列一个周期复杂度进行一些研究,并且主要讨论M序列一个周期复杂度的上下界,遍历性和分布情况。 注 本文在GF(2)上和n≥3情况下讨论。     

时间序列分解预测法及周期因素的探讨

本文运用时间序列分解预测法，分析门诊人次的变动规律，预测了季度门诊人次。本法与移动平均比率预测法相比，预测精度提高３１％。本文还探讨了时间序列分解预测的周期因素等有关问题。     

ESTIMATION OF THE MIXED AR AND HIDDEN PERIODIC MODEL

ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionGeneralizedhiddenperiodicmodelhasthefollowingformwhereacisthesetofallpositiveintegers,('~{((t);tEac}isastationarysequencewithzeromeanandcontinuousspectraldensity,i=n,qisanonnegativeinteger,'f=0,X=(Al,Az,',A,)isarealvectorwith--T相似文献   

Forecasting seasonal time series data: a Bayesian model averaging approach

A flexible Bayesian periodic autoregressive model is used for the prediction of quarterly and monthly time series data. As the unknown autoregressive lag order, the occurrence of structural breaks and their respective break dates are common sources of uncertainty these are treated as random quantities within the Bayesian framework. Since no analytical expressions for the corresponding marginal posterior predictive distributions exist a Markov Chain Monte Carlo approach based on data augmentation is proposed. Its performance is demonstrated in Monte Carlo experiments. Instead of resorting to a model selection approach by choosing a particular candidate model for prediction, a forecasting approach based on Bayesian model averaging is used in order to account for model uncertainty and to improve forecasting accuracy. For model diagnosis a Bayesian sign test is introduced to compare the predictive accuracy of different forecasting models in terms of statistical significance. In an empirical application, using monthly unemployment rates of Germany, the performance of the model averaging prediction approach is compared to those of model selected Bayesian and classical (non)periodic time series models.     

Hilbertian spatial periodically correlated first order autoregressive models

In this article, we consider Hilbertian spatial periodically correlated autoregressive models. Such a spatial model assumes periodicity in its autocorrelation function. Plausibly, it explains spatial functional data resulted from phenomena with periodic structures, as geological, atmospheric, meteorological and oceanographic data. Our studies on these models include model building, existence, time domain moving average representation, least square parameter estimation and prediction based on the autoregressive structured past data. We also fit a model of this type to a real data of invisible infrared satellite images.     

EWMA control charts for autoregressive processes

Many processes must be monitored by using observations that are correlated. An approach called algorithmic statistical process control can be employed in such situations. This involves fitting an autoregressive/moving average time series model to the data. Forecasts obtained from the model are used for active control, while the forecast errors are monitored by using a control chart. In this paper we consider using an exponentially weighted moving average (EWMA) chart for monitoring the residuals from an autoregressive model. We present a computational method for finding the out-of-control average run length (ARL) for such a control chart when the process mean shifts. As an application, we suggest a procedure and provide an example for finding the control limits of an EWMA chart for monitoring residuals from an autoregressive model that will provide an acceptable out-of-control ARL. A computer program for the needed calculations is provided via the World Wide Web.     

An efficient generalized least squares algorithm for periodic trended regression with autoregressive errors

Time series data with periodic trends like daily temperatures or sales of seasonal products can be seen in periods fluctuating between highs and lows throughout the year. Generalized least squares estimators are often computed for such time series data as these estimators have minimum variance among all linear unbiased estimators. However, the generalized least squares solution can require extremely demanding computation when the data is large. This paper studies an efficient algorithm for generalized least squares estimation in periodic trended regression with autoregressive errors. We develop an algorithm that can substantially simplify generalized least squares computation by manipulating large sets of data into smaller sets. This is accomplished by coining a structured matrix for dimension reduction. Simulations show that the new computation methods using our algorithm can drastically reduce computing time. Our algorithm can be easily adapted to big data that show periodic trends often pertinent to economics, environmental studies, and engineering practices.     

结构向量自回归时间序列的链图模型识别方法

本文研究了结构向量自回归时间序列的链图模型识别方法.利用局部密度估计法以及Bootstrap方法,给出了时间序列链图模型的概念以及模型结构识别方法.模拟结果显示本方法能有效地识别结构向量自回归模型变量问的相依关系.     

A Combinatorial Approach to Piecewise Linear Time Series Analysis

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.     

基于改进的BP网络对CET-4累计通过率时间序列的预测

时间序列并非总呈自相关性.与[4]不同,对本文中的CET-4累计通过率时间序列建立线性及二阶自回归模型,仿真计算失效.改进的BP网络,适用所有的一维时间序列.本文采用二步预测法,与其它采用BP网络对时间序列预测不同的是,本文不仅预测下一年的时间序列值,还将整个预测模型仿真出来,画出三维图形,从而为教务政策的制订提供直观易看、合理、客观的依据.     

The information matrices of the parameters of multiple mixed time series

Closed form matrix equations are given for the information matrix of the parameters of the vector mixed autoregressive moving average time series model.     

基于ARIMA与神经网络集成的GDP时间序列预测研究

本文深入分析了单整自回归移动平均(ARIMA)模型与神经网络(NN)模型的预测特性和优劣,并在此基础上建立了由ARIMA模型和NN模型集成的GDP时间序列预测模型与算法。其基本思想是充分发挥两种模型在线性空间和非线性空间的预测优势,据此将GDP时间序列的数据结构分解为线性自相关主体和非线性残差两部分,首先用ARIMA模型预测序列的线性主体,然后用NN模型对其非线性残差进行估计,最终集成为整个序列的预测结果。仿真实验表明:集成模型的预测准确率显著高于单一模型的预测准确率,从而证实了集成模型用于GDP预测的有效性。